Using an Atomic Force Microscope with an attachment for indentation, we have measured local, in vitro mechanical properties of healthy femoral artery tissue held in saline solution. The elastic modulus (34. 3 kPa) and viscoelastic response ({tau}sub{epsilon} {equals} 16.9 s and {tau}sub{sigma} {equals} 29.3 s) of the unstretched,intimal vessel wall have been determined using Sneddon theory and a three element model(standard linear solid) for viscoelastic materials. The procedures necessary to employ the indenting attachment to detect elastic moduli in the kPa range in liquid are described

Balooch, M.

Kinney, J.

Lilleodden, E.

Lundkvist, A.

Pruitt, L.

Sickhaus, W.

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February 9, 1998This is a preprint of a paper intended for publication in a journal or proceedings.  Sincechanges may be made before publication, this preprint is made available with theunderstanding that it will not be cited or reproduced without the permission of theauthor.LawrenceLivermoreNationalLaboratoryUCRL-JC-129779PREPRINTViscoelastic Properties of Healthy Human ArteryMeasured in Saline Solution by AFM-Based IndentationTechniqueThis paper was prepared for submittal to theMaterials Research Society Conference ProceedingsSan Francisco, CAApril 21-28, 1995A. Lundkvist, E. Lilleodden, W. Siekhaus, J. Kinney, L. Pruitt, M. BaloochDISCLAIMERThis document was prepared as an account of work sponsored by an agency ofthe United States Government.  Neither the United States Government nor theUniversity of California nor any of their employees, makes any warranty, expressor implied, or assumes any legal liability or responsibility for the accuracy,completeness, or usefulness of any information, apparatus, product, or processdisclosed, or represents that its use would not infringe privately owned rights.Reference herein to any specific commercial product, process, or service by tradename, trademark, manufacturer, or otherwise, does not necessarily constitute orimply its endorsement, recommendation, or favoring by the United StatesGovernment or the University of California.  The views and opinions of authorsexpressed herein do not necessarily state or reflect those of the United StatesGovernment or the University of California, and shall not be used for advertisingor product endorsement purposes.Viscoelastic Properties of Healthy Human Artery Measured in Saline Solution by AFM-Based Indentation TechniqueA. Lundkvist**, E. Lilleodden*, W. Siekhaus*, J. Kinney*, L. Pruitt** and M. Balooch** Lawrence Livermore National Laboratory, Livermore CA 94550, balooch1@llnl.gov** University of California, Berkeley CA 94720ABSTRACTUsing an Atomic Force Microscope with an attachment for indentation, we have measuredlocal, in vitro mechanical  properties of healthy femoral artery tissue held in saline solution.  Theelastic modulus (34.3 kPa) and viscoelastic response (τε = 16.9 s and τσ=29.3 s) of the unstretched,intimal vessel wall have been determined using Sneddon theory and a three element model(standard linear solid) for viscoelastic materials. The procedures necessary  to employ theindenting attachment to detect elastic moduli in the kPa range in liquid are described.INTRODUCTIONCoronary artery disease or atherosclerosis is the leading cause of death in the United States[1]. Percutaneous Transluminal Coronary Angioplasty (PTCA) is the most common treatment forpatients suffering from atherosclerosis. Although PTCA yields a greater than 90% immediatesuccess rate, the 30-40% restenosis rate, or re-narrowing of the coronary arteries, hinders completesuccess [2]. A significant portion of this restenosis rate is due to geometric remodeling of thediseased artery wall incurred during balloon inflation  (e.g. medial stretching [2], plaque dissection[3] and plaque compression [2,3]). If the plaque contains a significant amount of calcium deposits,preferential regions of high stress conducive to stretching or dissection may form during ballooninflation. Eighty percent of patients recommended for PTCA exhibit calcium deposits in the plaque[4]. Hence, there is particular clinical interest in understanding the local material properties andmechanical behavior of calcified atherosclerotic deposits and healthy arterial wall.The present work describes the technique of using the AFM-based nanoindenter todetermine the mechanical properties of s t tissues held in saline solution.  The static elasticmodulus and viscoelastic constants of the intimal surface of a healthy human femoral artery arereported. These results will be used as a base for further studies on atherosclerotic coronarytissues.EXPERIMENTAL TECHNIQUE AND RESULTSThe Atomic Force Microscope (small stage Nanoscope III, Digital Instruments, SantaBarbara, CA) has been modified by replacing the conventional head ssembly with a transducer-indenter assembly  called a Micromechanical Testing Instrument (Hysitron Inc., Minneapolis,MN).  Like its conventional counterpart, the instrument can image the topography of specimens bytracing the superficial contours of the sample with nano-Newton loads. In addition, the device is aforce-generating and depth-sensing  instrument (Nano-indenter) capable of generating  load-displacement  curves at specific locations in ambient and, with the corrections described here,liquid environments. The minimum load applied  is less than 1 µN and the maximumdisplacement  measured is 35 µm. Indenters  of varying materials (diamond, tungsten carbide,aluminum); shapes (Berkovich, spherical, flat cylindrical punch) and a range of diameters (.17 to2.0 mm) have been used for indentation of healthy human arteries.For the experiments reported  here, healthy femoral arteries supplied by the NationalDisease Research Interchange (NDRI) were scanned by intravascular ultrasound  (BostonScientific, Sunnyvale, CA) to ascertain that no plaque existed.  The vessel was cut longitudinally,sectioned in 5mm x 5mm regions and placed unstretched  in a .9% saline bath on the AFM stage.The basic components of the Micromechanical Testing Instrument are shown in Figure 1.The force recorded and  displayed by the instrument is defined as,Fdisplay = Aε 0V2d02(1)where A is the plate area, V is the voltage applied between the drive plate and pickup electrode, ε0is the dielectric constant and d0 is the spacing between the pickup electrode  and drive plat whenno weight (such as the indenter) is attached and no voltage is applied.  The vender specifies d0 as120 µm. In many material science applications, equation (1)  adequately represents the actual forceapplied to the material under investigation.membranePickupelectroded0 d1 xdinmembrane x+(d0-din)d0Drive plateSampleFigure 1.  Schematic of Micromechanical Testing I strument with parameters needed todetermine the actual force applied to soft materials in saline solution. The combination of pickupelectrode and drive plates is used to both generate a force, Fdisplay, and to measure displacement, x.For soft materials, however, the displacements could be large even for small appliedvoltages. In this case, the change in the plate spacing deviates substantially from that described byequation 1, and the force displayed does not equal the force actually applied to the sample.Additionally, the stiffness of the membrane, the weight of the indenter itself and the force exertedon the indenter’s shaft as a result of surface tension should be included to accurately describe theapplied force in liquid. The actual force applied to the sample isFa Fdisplayd0din -  x 2Ks x d0 din Fs.t. Mg= − + −( ) + + (2)where x is the displacement of the pickup electrode from its initial position din, Ks is the springconstant of the membrane (ignoring possible nonlinearity), Mg is the weight of the indenter andFs.t. is the force due to surface tension.  When a preload is applied to the sample, the force due tothe initial displacement  isPreload Ks dliq= − din 1 (3)In the absence of an initial preload, the  initial spacing, din, is replaced bydliq dairFs tKs1 1= − . .  (4)where  d1air is the spacing between the pickup electrode and drive plat in air due to the weight ofthe attached indenter (Figure 1).  Ks and d1air  are determined by making a best fit to displayedforce versus distance curves of several calibration runs done in air without a load applied to thesample. The results are shown in Figure 2a along with the deviation of experimental points fromthe optimum  fit. The experiments were repeated in liquid with no load applied to the sample toobtain Fs.t.. The result of the curve fit and its deviation from data points in liquid is shown inFigure 2b.05001000150020002500-40-200204060801000 5 10 15 20 25 30 35Load, µNExperimental Deviation, µNDisplacement, µm05001000150020002500-40-200204060801000 5 10 15 20 25 30 35 40Load, µNExperimental Deviation, µNDisplacement, µm         2a 2bFigure 2.  Displayed force vs. displacement with no load applied to the sample, and the deviationof experimental results from the optimum fit to force vs. displacement:  a) in air  b) in salinesolution.Since healthy human arteries are known to have high compliance, this tudy used a flatcircular punch consisting of a thin aluminum disk 2mm in diameter, attached to a stem of .5 mmdiameter  (to minimize surface tension forces) held by the mechanical testing instrument.  The“sine wave” appearance  of  the deviation of experimental results from the optimum fit to curvesof force vs. displacement evident  in  both air and  liquid  calibration runs in Figure 2 can beeliminated when a nonlinear  third-power term is added, as suggested by Timoshenko [5], todescribe the force vs. displacement  of the membrane.  The load accuracy of  the  measurements  is±10 µN in air and ± 20 µN in saline solution, and by almost a factor of two better when a nonlinearspring is considered.The data were analyzed using a simple three element model (standard linear solid [6])--aspring (µ0) placed in parallel with a Maxwell spring (µ1)-damper (η1) system.  The behavior ofthis model is characterized by three parameters:τε =η1µ1 ,       τσ =  η1µ0 1 + µ0µ1       and    ER =  µ02 r(5)where τε is the relaxation time for constant strain, τσ is the relaxation time for constant stress, r isthe indenter radius and ER is the relaxed elastic modulus of the system as time approaches infinity,based on contact stiffness and Sneddon indentation theory [7, 8].  The creep response [6], c(t), ofthis system to a constant force of magnitude unity, u(t), is  described asc(t) =  1µ0 1 − 1 − τετσ e− t τσ u(t) (6)The actual force and displacement vs. time for a healthy artery are shown in Figure 3.   Thinstrument was programmed to generate a trapezoidal “display-force” vs. time. Applying thecorrections described in equations (2) - (4) provided the time-dependent actual applied force shownin Figure 3.  A second order  polynomial was fit to the loading portion of the actual applied forcevs. time curve and this fitted analytic function, F(t), was integrated using the Boltzmannsuperposition principle for creep response given an arbitrary load profile [6].  This results in ananalytic displacement function, X(t), containing three undetermined model parameters µ0, τε andτ0.  X(t) = 1µ0 F(t) 0t − 1 − τετσ e− t τσ  e+ τ τσ0t∫  dF(τ)dτ  dτ (7)This function was then fit to the measured displacement during the loading-only portion of thedisplacement  vs. time data to determine  the model parameters. These parameters  were then usedin the Boltzmann  integral on the actual applied load curve F(t) to predict  the displacement vs. timedata, as plotted in figure 3.-200020040060080010001200-20246810120 50 100 150 200Actual LoadMeasuredDisplacementPredictedDisplacementActual Applied Load, µNDisplacement, µmTime, sFigure 3.  The actual force applied and measured displacement as a function of time for a h althy,femoral artery wall using a 2mm diameter, aluminum, flat punch. The Boltzmann superpositionprinciple was used to predict the displacement vs. time based on the Kelvin model parameters andthe time-dependent  loading curve.Table I compares the results of this study with previous indentation studies. Although the elasticmodulus values reported by Gow et al. [9, 10] were obtained with indenters smaller in diameterthan used here, information about the viscoelastic response is not provided.  The technique used byLee et al. [11] used a 7 mm diameter indenter, and hence the r sults represent an average over anarea more than 10 times larger than the area used in this study. In addition to providing localmeasurements of the elastic modulus of healthy, femoral artery (intimal) wall, to the best of theauthors’ knowledge, this investigation represents the first in vitro, localized assessment of theviscoelastic response of healthy inner arterial wall.Table I:     Comparison of Previous Indentation Studies with this Study (*)Aortic Intimal Non-Fibrous Aortic *Healthy FemoralSurface [9,10] Plaque Caps [11]   Intimal WallElastic Modulus (kPa)      90-152     41.2 ± 18.8         34.3τε    (sec)         ---             ---         16.9τσ    (sec)         ---             ---         29.3SUMMARY AND CONCLUSIONSThe add-on transducer to the standard AFM enhanced the capability of the instrument tomeasure local mechanical properties in addition to topographic imaging. To further increase itscapability for use on soft tissues held in aqueous solution one also needs to consider the forcesapplied to the indenter, such as weight and  surface tension, that are usually negligible for mostmaterials used in engineering applications. By considering these forces, the viscoelastic propertiesof an unstretched healthy artery wall in saline solution have been measured. To the authors’knowledge, there is no previous 3 parameter-based model of the mechanical response of theintimal layer of the artery wall.The instrumentation described here is being used with smaller indenters (.175 mmdiameter) to measure the static mechanical and viscoelastic response of healthy and diseasedarteries over a wide range of frequencies.  These investigations will provide a soundengineeringbasis for future balloon angioplasty studies, and will help to improve the design of other clinicaldevices used to treat patients with coronary artery disease.ACKNOWLEDGMENTSThis work was supported by the U.S. Department of Energy, through t e LDRD program atLawrence Livermore National Laboratory under contract No. W-7405-ENG-48.We want to thank Dr. W. Gerberich, U. of Minnesota, Dept. of Mechanical Engineering andMaterial Science; Dr. P. Yock, Stanford University Medical Center for Research in InterventionalCardiology; Greg Hyde, Guidant Corp., Advanced Cardiovascular Systems; and Dr. WayneBonin, Hysitron Inc. for their contributions to the scientific and technical substance of this paper.REFERENCES1. Heart and Stroke Facts:  1994 Statistical Supplement, American Heart Association.2. R. Virmani, A. Farb and A.P. Burke, American Heart Journal 127: 163-179 (1994).3. B.F. Waller, C.M. Orr, C.A. Pinkerton, J. Van Tassel, T. Peters and J.D. Slack,Journal of the American College of Cardiology 20 (3): 701-706 (1992).4. L.A. Fitzpatrick, A. Severson, W.D. Edwards and R.T. Ingram, Journal of ClinicalInvestigation 94: 1597-1604 (1994).5. S. P. Timoshenko and J. N. Goodier.    Theory of Elasticity   , 3rd edition. (McGraw HillBook Company, New York, 1970).6. Y.C. Fung,     Biomechanics   , 2nd ed. (Springer-Verlag New York, Inc., New York,1993), pp.41-46.7. I.N. Sneddon, International Journal of Engineering Science 3: 47 (1965).8. G.M Pharr, W.C. Oliver and F.R. Brotzen, Journal of Materials Research 7 (3): 613-617 (1992).9. B.S. Gow and R.N. Vaishnav, Journal of Applied Physiology 38 (2): 344-50 (1975).10. B.S. Gow, W.D. Castle and M.J. Legg, Journal of Biomechanics 16 (6): 451-458(1983).11.  R.T. Lee, G. Richardson, H.M. Loree, A.J. Grodzinsky, S.A. Gharib, F.J. Schoenand N. Pandian, Arteriosclerosis and Thrombosis 12 (1): 1-5 (1992).Technical Information Department  • Lawrence Livermore National LaboratoryUniversity of California • Livermore, California  94551

Viscoelastic properties of healthy human artery measured in saline solution by AFM based indentation technique

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Viscoelastic properties of healthy human artery measured in saline solution by AFM based indentation technique

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